As indicated in [1]}, [2]}, such permutation invariant functions can be obtained by combining the treatments of each color group vector \(V_j\)  with an additional "color-averaging" operation that performs an average of the features across the different color groups. It has notably been shown in [1]} that such operations are sufficient to recover all invariant functions from \(\mathcal {S}_k\)  to \(\mathbb {R}\) .
